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Papers by xingqiang xiu
arXiv (Cornell University), Feb 15, 2013
For an efficient implementation of Buchberger's Algorithm, it is essential to avoid the treatment... more For an efficient implementation of Buchberger's Algorithm, it is essential to avoid the treatment of as many unnecessary critical pairs or obstructions as possible. In the case of the commutative polynomial ring, this is achieved by the Gebauer-Möller criteria. Here we present an adaptation of the Gebauer-Möller criteria for non-commutative polynomial rings, i.e. for free associative algebras over fields. The essential idea is to detect unnecessary obstructions using other obstructions with or without overlap. Experiments show that the new criteria are able to detect almost all unnecessary obstructions during the execution of Buchberger's procedure.
Revista De La Union Matematica Argentina, Aug 5, 2019
A finite group G is called an MSN *-group if it is supersolvable, and all maximal subgroups of th... more A finite group G is called an MSN *-group if it is supersolvable, and all maximal subgroups of the Sylow subgroups of G are subnormal in G. A group G is called a minimal non-MSN *-group if every proper subgroup of G is an MSN *-group but G itself is not. In this paper, we obtain a complete classification of minimal non-MSN *-groups.
Elementary Theory of Groups and Group Rings, and Related Topics, 2020
Revista de la Unión Matemática Argentina, 2019
A finite group G is called an MSN *-group if it is supersolvable, and all maximal subgroups of th... more A finite group G is called an MSN *-group if it is supersolvable, and all maximal subgroups of the Sylow subgroups of G are subnormal in G. A group G is called a minimal non-MSN *-group if every proper subgroup of G is an MSN *-group but G itself is not. In this paper, we obtain a complete classification of minimal non-MSN *-groups.
For an efficient implementation of Buchberger's Algorithm, it is essential to avoid the treatment... more For an efficient implementation of Buchberger's Algorithm, it is essential to avoid the treatment of as many unnecessary critical pairs or obstructions as possible. In the case of the commutative polynomial ring, this is achieved by the Gebauer-Möller criteria. Here we present an adaptation of the Gebauer-Möller criteria for non-commutative polynomial rings, i.e. for free associative algebras over fields. The essential idea is to detect unnecessary obstructions using other obstructions with or without overlap. Experiments show that the new criteria are able to detect almost all unnecessary obstructions during the execution of Buchberger's procedure.
De Gruyter eBooks, Feb 10, 2020
arXiv (Cornell University), Feb 15, 2013
For an efficient implementation of Buchberger's Algorithm, it is essential to avoid the treatment... more For an efficient implementation of Buchberger's Algorithm, it is essential to avoid the treatment of as many unnecessary critical pairs or obstructions as possible. In the case of the commutative polynomial ring, this is achieved by the Gebauer-Möller criteria. Here we present an adaptation of the Gebauer-Möller criteria for non-commutative polynomial rings, i.e. for free associative algebras over fields. The essential idea is to detect unnecessary obstructions using other obstructions with or without overlap. Experiments show that the new criteria are able to detect almost all unnecessary obstructions during the execution of Buchberger's procedure.
Revista De La Union Matematica Argentina, Aug 5, 2019
A finite group G is called an MSN *-group if it is supersolvable, and all maximal subgroups of th... more A finite group G is called an MSN *-group if it is supersolvable, and all maximal subgroups of the Sylow subgroups of G are subnormal in G. A group G is called a minimal non-MSN *-group if every proper subgroup of G is an MSN *-group but G itself is not. In this paper, we obtain a complete classification of minimal non-MSN *-groups.
Elementary Theory of Groups and Group Rings, and Related Topics, 2020
Revista de la Unión Matemática Argentina, 2019
A finite group G is called an MSN *-group if it is supersolvable, and all maximal subgroups of th... more A finite group G is called an MSN *-group if it is supersolvable, and all maximal subgroups of the Sylow subgroups of G are subnormal in G. A group G is called a minimal non-MSN *-group if every proper subgroup of G is an MSN *-group but G itself is not. In this paper, we obtain a complete classification of minimal non-MSN *-groups.
For an efficient implementation of Buchberger's Algorithm, it is essential to avoid the treatment... more For an efficient implementation of Buchberger's Algorithm, it is essential to avoid the treatment of as many unnecessary critical pairs or obstructions as possible. In the case of the commutative polynomial ring, this is achieved by the Gebauer-Möller criteria. Here we present an adaptation of the Gebauer-Möller criteria for non-commutative polynomial rings, i.e. for free associative algebras over fields. The essential idea is to detect unnecessary obstructions using other obstructions with or without overlap. Experiments show that the new criteria are able to detect almost all unnecessary obstructions during the execution of Buchberger's procedure.
De Gruyter eBooks, Feb 10, 2020